Simplify the following expression: $z = \dfrac{-9p^2 + 81p + 90}{p - 10} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ z =\dfrac{-9(p^2 - 9p - 10)}{p - 10} $ Then we factor the remaining polynomial: $p^2 {-9}p {-10} $ ${-10} + {1} = {-9}$ ${-10} \times {1} = {-10}$ $ (p {-10}) (p + {1}) $ This gives us a factored expression: $\dfrac{-9(p {-10}) (p + {1})}{p - 10}$ We can divide the numerator and denominator by $(p + 10)$ on condition that $p \neq 10$ Therefore $z = -9(p + 1); p \neq 10$